Mechanics of the Finite Deformation Behavior of Biomacromolecular
Networks

Mary C. Boyce

Department of Mechanical Engineering

Massachusetts Institute of Technology

Cambridge,
MA

Abstract

The
force-extension behavior of many biomacromolecules is known to exhibit a
characteristic repeating pattern of a nonlinear rise in force with imposed displacement
to a peak, followed by a significant force drop upon reaching the peak (a "saw-tooth"
pattern) due to stretch-induced unfolding of modules along the molecular chain.
This behavior is speculated to play a governing role in the function of
biological materials and structure. In this paper, models for the mechanical
behavior of single modular macromolecules and networks of such macromolecules
are developed enabling understanding of the manner in which this characteristic
single molecule behavior is translated to the behavior of molecular strands,
membranes, and solids. Single molecule force-extension behavior is modeled
using the Freely-Jointed Chain and Worm-Like Chain models of statistical
mechanics together with a new unfolding criterion based on the orientation
distribution of folded modules. The single molecule behavior is then used within
a continuum mechanics framework to construct constitutive models of the finite deformation
stress-strain behavior of two- and three-dimensional networks of modular biomacromolecules.
The proposed planar network model has applicability to biological membrane
skeletons and the three-dimensional network model emulates cytoskeletal networks
and solid biological tissues containing modular macromolecules. Simulation of the
multiaxial stress-strain behavior of these networks illustrates the macroscopic
membrane and solid stretching conditions which activate unfolding in these microstructures.
The models simultaneously track the evolution in underlying microstructural
features with different macroscopic stretching conditions, including the evolution
in molecular orientation and the number of folded and unfolded modules. One
role of this behavior in biological materials is illustrated in a study of the
tensile deformation of nacre where the unfolding behavior of the organic matrix
molecules is found to mitigate load transfer to the mineral tablets and thus
provide enhanced strain to failure and toughness of the biocomposite nacre
material over that of the bulk mineral.